# Betti number

Let $X$ denote a topological space, and let $H_{k}(X,\mathbb{Z})$ denote the $k$-th homology group of $X$. If $H_{k}(X,\mathbb{Z})$ is finitely generated, then its rank is called the $k$-th Betti number of $X$.

Title Betti number BettiNumber 2013-03-22 13:47:14 2013-03-22 13:47:14 mathcam (2727) mathcam (2727) 6 mathcam (2727) Definition msc 55N10 homology HomologyTopologicalSpace